Geodesic
Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 1, pp. 49-75
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a charged quantum particle moving in a two-dimensional plane in the three-dimensional coordinate space and scattering on an immovable Coulomb center in the same plane. We derive and investigate expansions of the wave function and of all radial wave functions of the particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic in the low-energy limit.
Keywords: two-dimensional Coulomb scattering, wave function, low-energy asymptotic behavior. 
@article{TMF_2016_188_1_a3,
     author = {V. V. Pupyshev},
     title = {Two-dimensional {Coulomb} scattering of a~quantum particle: {Low-energy} asymptotic behavior},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {49--75},
     year = {2016},
     volume = {188},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a3/}
}
TY  - JOUR
AU  - V. V. Pupyshev
TI  - Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 49
EP  - 75
VL  - 188
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a3/
LA  - ru
ID  - TMF_2016_188_1_a3
ER  - 
%0 Journal Article
%A V. V. Pupyshev
%T Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 49-75
%V 188
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a3/
%G ru
%F TMF_2016_188_1_a3
V. V. Pupyshev. Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 1, pp. 49-75. http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a3/

[1] H. Friedrich, Scattering Theory, Lecture Notes in Physics, 872, Springer, Berlin, 2013 | DOI | MR | Zbl

[2] B. Zaslow, M. E. Zandler, Amer. J. Phys., 35:12 (1967), 1118–1119 | DOI

[3] X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, W. Y. Ching, Phys. Rev. A, 43:3 (1991), 1186–1196 | DOI | MR

[4] S. H. Guo, X. L. Yang, F. T. Chan, K. W. Wong, W. Y. Ching, Phys. Rev. A, 43:3 (1991), 1197–1205 | DOI | MR

[5] R. E. Moss, Amer. J. Phys., 55:5 (1987), 397–311 | DOI

[6] M. Robnik, V. G. Romanovski, J. Phys. A: Math. Gen., 36:29 (2003), 7923–7951 | DOI | MR | Zbl

[7] G. Barton, Amer. J. Phys., 51:5 (1983), 420–422 | DOI

[8] D. Yafaev, J. Phys. A: Math. Gen., 30:19 (1997), 6981–6992 | DOI | MR | Zbl

[9] Q.-G. Lin, Phys. Lett. A, 260:1–2 (1999), 17–23, arXiv: quant-ph/9910044 | DOI | MR | Zbl

[10] W. Dittrich, Amer. J. Phys., 67:9 (1999), 768–775, arXiv: physics/9902070 | DOI

[11] V. V. Pupyshev, TMF, 186:2 (2016), 252–271 | DOI | MR | Zbl

[12] V. V. Pupyshev, TMF, 186:1 (2016), 123–141 | DOI | DOI | MR | Zbl

[13] V. I. Smirnov, Kurs vysshei matematiki, v. 1, Nauka, M., 1974 | MR | Zbl

[14] B. M. Budak, S. V. Fomin, Kratnye integraly i ryady, Fizmatlit, M., 2002 | MR | Zbl

[15] M. B. Fedoryuk, Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | DOI | MR | MR | Zbl

[16] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 1, Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973 | MR | Zbl

[17] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR | MR | Zbl

[18] Yu. Lyuk, Spetsialnye matematicheskie fuktsii i ikh approksimatsii, Mir, M., 1980 | MR | Zbl

[19] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 ; Интегралы и ряды. Специальные функции, Наука, М., 1983 | MR | Zbl | MR | Zbl

[20] C.-E. Fröberg, Rev. Modern Phys., 27:4 (1955), 399–411 | DOI | MR | Zbl

[21] Z. Idziaszek, T. Calarso, P. Zoller, Phys. Rev. A, 76:3 (2007), 033409, 16 pp. | DOI